Meaning "I write" and "I'm writing" are both translated the same, for example: escribo, j'ecris, يكتب.

I can't speak French, but you can certainly say "estoy escribiendo", in Spanish if you mean you are writing right now. Similarly, you can say "أنا كاتب" in Fusha Arabic, which is usually translated as "I'm writing", although it is not exactly the same, because it could also mean "I'm a writer". In addition, there are some forms in dialects to express that idea, for example in Moroccan Darija you could say "كنكتب" (I'm writing) in contrast to "نكتب" (I write).

EDIT: However, I wouldn't use a continuous form to talk about a past (like "have been VERB-ing" in English), but I'd rather use a normal past tense (madi).

Well, I don't know in American Spanish, but in Spain it is absolutely common and completely right. As far as I know it is as in English, I mean, "Escribo todos los días" vs. "Estoy escribiendo ahora mismo". However, it is true that you could hear the simple present some times when the continuous form would be used, for example, someone calls you and asks "¿Qué haces?", but then you answer "Estoy viendo la tele." Anyway, the question could possibly be "¿Qué estás haciendo?" too.

The reason I compared them is because I had assumed all the present tenses in Arabic were the same...at least I had thought as much since Arabic works off the perfect/imperfect system.

Yes, you're right. But you can also use other options to express more concretely the tenses, such as particles or, as in this case, the active participle (I'm not sure if it's called like that in English, but I mean the form فاعل).

Well, I don't know in American Spanish, but in Spain it is absolutely common and completely right. As far as I know it is as in English, I mean, "Escribo todos los días" vs. "Estoy escribiendo ahora mismo". However, it is true that you could hear the simple present some times when the continuous form would be used, for example, someone calls you and asks "¿Qué haces?", but then you answer "Estoy viendo la tele." Anyway, the question could possibly be "¿Qué estás haciendo?" too.

I must say I've always been shocked by the parallelism between the "present" vs. the "present progressive" tenses in both English and Spanish.

Now if in traditional Spanish grammar, estar + gerundio is always analyzed as a verbal periphrasis and not as a "compound tense" (as it is in English), that's another matter.

The reason I compared them is because I had assumed all the present tenses in Arabic were the same...at least I had thought as much since Arabic works off the perfect/imperfect system.

Yes, you're right. But you can also use other options to express more concretely the tenses, such as particles or, as in this case, the active participle (I'm not sure if it's called like that in English, but I mean the form فاعل).

Yes, that's how it's usually called in English.

Actually, all this time I've been studying Arabic using English-language books only. Would you mind telling me how it's usually called in Spanish (if you happen to know)?

Something important to mention about this use of اسم الفاعل (the active particple), is that it has no sense of time. In أنا فاعله, it could stand equally for a "past progressive" ("I was doing it", although كنت أفعله kuntu ’afʕalu-hu would probably be more common here (and yes, Arabic has a few "compound tenses")), "present progressive" ("I'm doing it") or "future progressive" ("I will be doing it").

Now if in traditional Spanish grammar, estar + gerundio is always analyzed as a verbal periphrasis and not as a "compound tense" (as it is in English), that's another matter.

Yep, I forgot to mention that.

Would you mind telling me how it's usually called in Spanish (if you happen to know)?

Just as in English, "participio activo", I'm sure this term comes from the study of the grammar of classical languages, since in Arabic grammar it's called اسم الفاعل just because of the form it has, likewise the object of a sentence is called مفعول به, they have a quite simple way of describing grammatical terms.

In أنا فاعله, it could stand equally for a "past progressive" ("I was doing it", although كنت أفعله kuntu ’afʕalu-hu would probably be more common here (and yes, Arabic has a few "compound tenses")), "present progressive" ("I'm doing it") or "future progressive" ("I will be doing it").

Yes, and there are even compound tenses with كان + مرفوع. It isn't actually so different as it seems when you read it for the first time .

Also, what's the Arabic translation of these phrases?I am waitingI thoughtLoving you isI just want you to knowAnd allow me toAm I present in your dream?Am I present in your heart?I have sang my sad tunesSymphony only for you